Simplify the expression and answer the following: a. What is the resulting coefficient of \( a^{2} \) ? b. What is the resulting coefficient of \( a^{3} b^{2} \) ? \( \left(15 a^{2}-a^{3} b^{2}-9 b^{3}\right)+\left(-10 a^{3} b^{2}-11 a^{2}-b^{2}+25 a\right. \) a. Coefficient of \( a^{2}= \) b. Coefficient of \( a^{3} b^{2}= \)

1. Write the expression: \[ \left(15 a^{2} - a^{3} b^{2} - 9 b^{3}\right) + \left(-10 a^{3} b^{2} - 11 a^{2} - b^{2} + 25 a\right) \] 2. Combine like terms: - For \( a^{2} \): \[ 15a^{2} + (-11a^{2}) = 4a^{2} \] - For \( a^{3} b^{2} \): \[ -a^{3} b^{2} + (-10a^{3} b^{2}) = -11a^{3} b^{2} \] - Other terms remain separate as they do not mix with \( a^{2} \) or \( a^{3} b^{2} \). 3. Therefore, the simplified expression includes: \[ 4a^{2} \quad \text{and} \quad -11a^{3} b^{2} \] 4. Answers: a. The resulting coefficient of \( a^{2} \) is \( 4 \). b. The resulting coefficient of \( a^{3} b^{2} \) is \( -11 \).